NONLINEAR AMPLIFICATION OF STATIONARY ROSSBY WAVES NEAR RESONANCE .1.

The authors search the stationary solutions of the barotropic vorticit y equation in spherical coordinates by numerically solving the equatio ns with the Newton-Keller pseudoarclength continuation method. The sol utions consist of planetary-scale Rossby waves superimposed on zonal w ind profiles and forced by sinusoidal orography in near-resonance cond itions. By varying the zonal wind strength across resonance, it is sho wn that multiple solutions with different wave amplitudes can be found : for small forcing and dissipation, the solution curve is the well-kn own bended resonance. The comparison between numerical results and the oretical predictions by a previously developed weakly nonlinear theory is successfully attempted. The authors then extend the barotropic, we akly nonlinear theory to stationary Rossby waves forced by large-scale orography and dissipated by Ekman friction at the surface, in the fra mework of the quasigeostrophic model continuous in the vertical direct ion. The waves are superimposed on vertical profiles of zonal wind and stratification parameters taken from observations of the wintertime N orthern Hemisphere circulation. In near-resonant conditions, the weakl y nonlinear theory predicts multiple amplitude equilibration of the ed dy field for a fixed vertical profile of the zonal wind. The authors d iscuss the energetics of the stationary waves and show that the form d rag and Ekman dissipation can be made very small even if realistic val ues of the parameters are taken, at variance with the barotropic case. This model is proposed as the theoretical base for such phenomena as atmospheric blocking, bimodality, and weather regimes.